{"paper":{"title":"The cut-off resolvent can grow arbitrarily fast in obstacle scattering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Siavash Sadeghi, Simon N. Chandler-Wilde","submitted_at":"2025-08-23T09:18:51Z","abstract_excerpt":"We consider time-harmonic acoustic scattering by a compact sound-soft obstacle $\\Gamma\\subset \\mathbb{R}^n$ ($n\\geq 2$) that has connected complement $\\Omega := \\mathbb{R}^n\\setminus \\Gamma$. This scattering problem is modelled by the inhomogeneous Helmholtz equation $\\Delta u + k^2 u = -f$ in $\\Omega$, the boundary condition that $u=0$ on $\\partial \\Omega = \\partial \\Gamma$, and the standard Sommerfeld radiation condition. It is well-known that, if the boundary $\\partial \\Omega$ is smooth, then the norm of the cut-off resolvent of the Laplacian, that maps the compactly supported inhomogeneous"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.16958","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}